With the advent of high precision photometry from satellites such as Kepler and CoRoT, a whole new layer of interesting and astounding astronomical objects has been revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccen- tric ellipsoidal variables that undergo strong tidal interactions when the stars are almost in contact at the time of closest approach. These interactions deform of the stars and cause a notable light curve variation in the form of a tidal pulse. A subset of these objects (∼20%) show prominent tidally induced pulsations: pulsations forced by the binary orbit. We now have a fully functional code that models binary star features (using phoebe) and stellar pulsations simultaneously, enabling a complete and accurate heartbeat star model to be determined. In this paper we show the results of our new code, which uses emcee, a variant of mcmc, to generate a full set of stellar parameters. We further highlight the interesting features of KIC 8164262, including its tidally induced pulsations and resonantly locked pulsations

Ballot, J

Fuller, J

García, RA

Hambleton, K

Kurtz, DW

Prsa, A

Thompson (SU), S

EPJ Web of Conferences

English

CLoK

Heartbeat Stars and The Ringing of Tidal PulsationsKelly Hambleton1,2,a, Don Kurtz1, Andrej Prsˇa2, Jim Fuller3, and Susan Thompson4,51 Jeremiah Horrocks Institute, University of Central Lancashire, Fylde Road, Preston, Lancashire,PR1 2HE England2 Department of Astrophysics and Planetary Science, Villanova University, 800 East Lancaster Av-enue, Villanova, PA 19085 USA3 California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125 USA4 NASA Ames Research Center, Moﬀett Field, CA 94035, USA5 SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain View, CA 94043, USA.Abstract. With the advent of high precision photometry from satellites such as Keplerand CoRoT, a whole new layer of interesting and astounding astronomical objects hasbeen revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccen-tric ellipsoidal variables that undergo strong tidal interactions when the stars are almost incontact at the time of closest approach. These interactions deform of the stars and cause anotable light curve variation in the form of a tidal pulse. A subset of these objects (∼20%)show prominent tidally induced pulsations: pulsations forced by the binary orbit. We nowhave a fully functional code that models binary star features (using phoebe) and stellarpulsations simultaneously, enabling a complete and accurate heartbeat star model to bedetermined. In this paper we show the results of our new code, which uses emcee, a variantof mcmc, to generate a full set of stellar parameters. We further highlight the interestingfeatures of KIC 8164262, including its tidally induced pulsations and resonantly lockedpulsations.1 IntroductionIn close binary systems, the tidal interactions between the stellar components cause the stars to becomedistorted and prolate, with the point of the star extending towards the companion. Consequently, asthe stars progress around the orbit and the stellar proﬁle and temperature distribution over the starchanges, we observe variations in the stellar ﬂux. When combined with luminosity variations producedby reﬂection and Doppler boosting, this phenomenon is known as ellipsoidal variation. In circularsystems the light varies periodically, twice per orbit. In eccentric systems, such as heartbeat stars, thesame physical principles apply, although due to the varying distance between the stars over the orbit,the stellar shapes are also constantly changing, with the most signiﬁcant change occurring when thestars are at closest approach. Thus, in these systems, the dominant variation in the light curve (knownas the periastron variation or heartbeat) occurs once per orbital cycle at periastron.The ﬁrst heartbeat star, KOI-54 (depicted in the top panel of Fig. 1), was discovered using theKepler satellite (1). Shortly after, many more discoveries were made including those by Thompson etal. (2), who published a catalogue of 17 heartbeat stars from the Kepler ﬁeld; Nicholls & Wood (3),who identiﬁed seven heartbeat stars in the Large Magellanic Cloud using the OGLE survey; and morerecently in the Kepler binary catalogue 3 paper (Kirk et al. 2014, in prep.), an extensive catalogueof binary stars that contains 154 heartbeat stars, all observed using the Kepler satellite. Fig. 1 showsa selection of heartbeat stars from the Kepler sample. These heartbeat stars were identiﬁed througha e-mail: kmhambleton@uclan.ac.uk    DOI: 10.1051/C©Owned by the authors, published by EDP Sciences, 2015/0 0 (  2015)201epjconfEPJ Web of Conferences ,5 0 01011010044	 !77Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510104007Fig. 1. A selection of heartbeat stars from the Kepler sample. Depicted are the time series (left panel) and phasefolded data (right panel). The phase folded data clearly depict the pulsations that are integer multiples of theorbital frequency: tidally induced pulsations.a combined eﬀort from the Heartbeat Star Team, the Planet Hunters, the Eclipsing Binary WorkingGroup and other independent sources.2 Tidally Induced PulsationsTidally induced pulsations are stellar oscillations that are driven by the tidal force of the companionstar. In a binary system with an eccentric orbit, when a stellar eigenfrequency is close to a multiple ofthe orbital frequency, the star can act like a forced oscillator, which causes an increase in the oscillationamplitude of the mode (relative to non-resonant modes). The signature of tidally excited modes isthus an oscillation frequency at a precise integer multiple of the orbital frequency. Approximately20% of our current Kepler sample of heartbeat stars demonstrate tidally induced pulsations above ourdetection limit.Tidally induced pulsations have long been theorised (4; 5; 6) as a mechanism for the circulari-sation of binary star orbits and the spin up of stars. However, until KOI-54, their presence has onlybeen speculated (7). The unquestionable nature of the tidally induced pulsations in KOI-54 sparkedthe interest of many theorists and consequently three publications (8; 9; 10) appeared discussing thephysical nature of tidally induced pulsations and the relevance of the 90th and 91st orbital harmonic- the two prominent pulsation frequencies in KOI-54. Fuller & Lai (8) proposed that the two highestamplitude tidally induced pulsations were excited through a mechanism called resonant locking (cf.§2.1). Burkart et al. (9) disputed this on the grounds that the torque produced by the proposed modeswas not enough to provide resonant locks and that it is unlikely that two resonant locks would occursimultaneously. Later, O’leary & Burkart (10) showed that the 90th and 91st harmonic were likelyl = 2,m = 0 modes, which theory at the time suggested could not be resonantly locked. Anotherinteresting observation by O’leary & Burkart (10) was that all of the pulsation modes of KOI-54 areEPJ Web of Conferences04007-p.2either tidally excited pulsations or their combinations, which was later found to be the case for all thegravity (g) modes in KIC 4544587 (11).2.1 Resonant LockingThe theory of resonantly excited modes – eigenmodes in resonance with the orbit – was suggested byWitte and Savonije (12; 13) and again more recently by Kumar, Ao and Quataert (14) long before thediscovery of heartbeat stars. Due to the expected transient nature of resonant modes, it was not antic-ipated that they would be observed. However, KOI-54 and KIC 8164262 (cf. Sect. 4) both have highamplitude modes that are not easily explained by the forcing of the eigenfrequencies alone. Resonancelocking has been proposed as a mechanism that can “lock” a stellar eigenfrequency and the orbit inresonance, thus extending the lifetime of the resonance and making observations of tidal resonancepossible. While the resonant locking of KOI-54 is currently under dispute, it has not been completelyruled out. Moreover, KIC 8164262 has only a single high amplitude mode that is an l = 2,m = 2 mode,which makes a stronger case for resonant locking.The proposed mechanism of resonant locking is the following: as two stars in an eccentric conﬁgu-ration orbit each other, the stellar orbit evolves through the transfer of energy and angular momentum,causing the orbit and thus orbital period to get smaller and the stars spin faster. In parallel, the increasein rotational velocity of the stars causes the stellar eigenfrequencies to change. Resonance lockingpredicts that, when in resonance, these two eﬀects happen on an equal time scale such that the stellareigenfrequencies are locked to the changing orbital period. Thus, rather than passing through reso-nance the tidally induced pulsations are locked in resonance with the orbit, enabling the observationof resonantly excited modes.3 Modelling Heartbeat StarsAs the parameter space of binary stars is highly irregular with many degeneracies and correlations,we chose to combine emcee, an aﬃne invariant version of Markov chain Monte Carlo methods (mcmc)(15) with phoebe, the binary modelling software package, which now has python scripting capabilities.When modelling heartbeat stars we also ﬁt the tidally induced pulsations using sine waves by ﬁxingthe frequencies to a multiples of the orbital frequency and ﬁtting the amplitudes and phases.To reduce the number of parameters in our models, at each iteration we calculate: the phase of theperiastron variation, the passband luminosity and the spin to orbital rotation frequency. To enhanceour models we also calculate the critical potentials at the Lagrangian points L1 and L2. Subsequently,if there is no evidence of mass transfer, we use this as a constraint for our models and do not allowthe potential value to become smaller than the potential at the Lagrangian point L1. Alternatively, ifthere is evidence of mass transfer (or for contact systems), we do not allow the stellar potentials tobecome smaller than L2 as this creates a non-physical scenario where the model star has a dimple inthe side pointing away from the companion. The common geometry of heartbeat stars also make themideal candidates for Doppler boosting. Consequently we adjust the model ﬂux to account for Dopplerboosting using Eqn. 2 in Bloemen et al. (16), extended to account for boosting in both objects.4 KIC8164262KIC 8164262 is a highly eccentric (e ≈ 0.9), 13th magnitude heartbeat star in a ∼90 d orbit witha single high amplitude (∼900 ppm) tidally induced pulsation that oscillates precisely 229 times perorbit (cf. Fig.2). The primary component of KIC 8164262 is a late A/early F star with an M typecompanion. This object was selected for detailed study as the prominent high amplitude mode wassuggestive of resonant locking. KIC 8164262 presents a plethora of tidally induced g modes rangingfrom 120 to 320 cycles per orbit (∼1–4 d−1). However, the largest amplitude mode has an amplitudetwenty times greater than all other modes (900 ppm compared to the second highest at 45 ppm). We04007-p.3The Space Photometry Revolution 0.9980.9991.0001.0011.002Flux-0.0010.0000.001-0.02 -0.01 0.00 0.01 0.02PhaseFig. 2. Upper panel: A phased light curve (black points) of KIC 8164262, a heartbeat star with a single highamplitude pulsation. The model is overlayed in red and is comprised of the binary features and highest amplitudepulsation. The periastron variation, centred on zero, has a similar amplitude to the highest amplitude pulsation.Lower panel: the residuals of the binary model ﬁt to the phased data (black points). Only a fraction of the 90 dorbit is shown for clarity.used theoretical models of a star with equal mass (M1 = 1.9M), radius (R1 = 2.5R) and temperature(Te f f ,1 = 7000K) to predict the expected combinations of frequency and amplitudes for resonantlylocked modes. These predictions are in good agreement with the frequency and amplitude of the 229thharmonic.References1. W.F. Welsh, J.A. Orosz, C. Aerts, T.M. Brown, E. Brugamyer, W.D. Cochran, R.L. Gilliland, J.A.Guzik, D.W. Kurtz, D.W. Latham et al., ApJS197, 4 (2011), 1102.17302. S.E. Thompson, M. Everett, F. Mullally, T. Barclay, S.B. Howell, M. Still, J. Rowe, J.L. Chris-tiansen, D.W. Kurtz, K. Hambleton et al., ApJ753, 86 (2012), 1203.61153. C.P. Nicholls, P.R. Wood, MNRAS421, 2616 (2012), 1201.10434. J.P. Zahn, A&A41, 329 (1975)5. P. Goldreich, P.D. Nicholson, ApJ342, 1079 (1989)6. M.G. Witte, G.J. Savonije, A&A386, 222 (2002)7. C. Maceroni, J. Montalba´n, E. Michel, P. Harmanec, A. Prsa, M. Briquet, E. Niemczura, T. Morel,D. Ladjal, M. Auvergne et al., A&A508, 1375 (2009), 0910.35138. J. Fuller, D. Lai, MNRAS420, 3126 (2012), 1107.45949. J. Burkart, E. Quataert, P. Arras, N.N. Weinberg, MNRAS421, 983 (2012), 1108.382210. R.M. O’Leary, J. Burkart, MNRAS440, 3036 (2014), 1308.001611. K.M. Hambleton, D.W. Kurtz, A. Prsˇa, J.A. Guzik, K. Pavlovski, S. Bloemen, J. Southworth,K. Conroy, S.P. Littlefair, J. Fuller, MNRAS434, 925 (2013), 1306.181912. M.G. Witte, G.J. Savonije, A&A350, 129 (1999), astro-ph/990907313. M.G. Witte, G.J. Savonije, A&A366, 840 (2001)14. P. Kumar, C.O. Ao, E.J. Quataert, ApJ449, 294 (1995), arXiv:astro-ph/950305315. D. Foreman-Mackey, D.W. Hogg, D. Lang, J. Goodman, PASP125, 306 (2013), 1202.366516. S. Bloemen, T.R. Marsh, R.H. Østensen, S. Charpinet, G. Fontaine, P. Degroote, U. Heber, S.D.Kawaler, C. Aerts, E.M. Green et al., MNRAS410, 1787 (2011), 1010.2747EPJ Web of Conferences04007-p.4

Heartbeat stars and the ringing of tidal pulsations

With the advent of high precision photometry from satellites such as Kepler and CoRoT, a whole new layer of interesting and astounding astronomical objects has been revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccentric ellipsoidal variables that undergo strong tidal interactions when the stars are almost in contact at the time of closest approach. These interactions deform of the stars and cause a notable light curve variation in the form of a tidal pulse. A subset of these objects (~20%) show prominent tidally induced pulsations: pulsations forced by the binary orbit. We now have a fully functional code that models binary star features (using PHOEBE) and stellar pulsations simultaneously, enabling a complete and accurate heartbeat star model to be determined. In this paper we show the results of our new code, which uses emcee, a variant of mcmc, to generate a full set of stellar parameters. We further highlight the interesting features of KIC 8164262, including its tidally induced pulsations and resonantly locked pulsations

Hambleton Kelly

Kurtz Don

Prša Andrej

Fuller Jim

Thompson Susan

Directory of Open Access Journals

Heartbeat Stars and the Ringing of Tidal Pulsations

Kelly Hambleton

Don Kurtz

Andrej Prša

Jim Fuller

Susan Thompson

Crossref

Hambleton, Kelly

Kurtz, Don

Prša, Andrej

Fuller, Jim

Thompson, Susan

Caltech Authors - Main

Heartbeat Stars and The Ringing of Tidal Pulsations
Kelly Hambleton1,2,a, Don Kurtz1, Andrej Prsˇa2, Jim Fuller3, and Susan Thompson4,5
1 Jeremiah Horrocks Institute, University of Central Lancashire, Fylde Road, Preston, Lancashire,
PR1 2HE England
2 Department of Astrophysics and Planetary Science, Villanova University, 800 East Lancaster Av-
enue, Villanova, PA 19085 USA
3 California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125 USA
4 NASA Ames Research Center, Moﬀett Field, CA 94035, USA
5 SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain View, CA 94043, USA.
Abstract. With the advent of high precision photometry from satellites such as Kepler
and CoRoT, a whole new layer of interesting and astounding astronomical objects has
been revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccen-
tric ellipsoidal variables that undergo strong tidal interactions when the stars are almost in
contact at the time of closest approach. These interactions deform of the stars and cause a
notable light curve variation in the form of a tidal pulse. A subset of these objects (∼20%)
show prominent tidally induced pulsations: pulsations forced by the binary orbit. We now
have a fully functional code that models binary star features (using phoebe) and stellar
pulsations simultaneously, enabling a complete and accurate heartbeat star model to be
determined. In this paper we show the results of our new code, which uses emcee, a variant
of mcmc, to generate a full set of stellar parameters. We further highlight the interesting
features of KIC 8164262, including its tidally induced pulsations and resonantly locked
pulsations.
1 Introduction
In close binary systems, the tidal interactions between the stellar components cause the stars to become
distorted and prolate, with the point of the star extending towards the companion. Consequently, as
the stars progress around the orbit and the stellar proﬁle and temperature distribution over the star
changes, we observe variations in the stellar ﬂux. When combined with luminosity variations produced
by reﬂection and Doppler boosting, this phenomenon is known as ellipsoidal variation. In circular
systems the light varies periodically, twice per orbit. In eccentric systems, such as heartbeat stars, the
same physical principles apply, although due to the varying distance between the stars over the orbit,
the stellar shapes are also constantly changing, with the most signiﬁcant change occurring when the
stars are at closest approach. Thus, in these systems, the dominant variation in the light curve (known
as the periastron variation or heartbeat) occurs once per orbital cycle at periastron.
The ﬁrst heartbeat star, KOI-54 (depicted in the top panel of Fig. 1), was discovered using the
Kepler satellite (1). Shortly after, many more discoveries were made including those by Thompson et
al. (2), who published a catalogue of 17 heartbeat stars from the Kepler ﬁeld; Nicholls & Wood (3),
who identiﬁed seven heartbeat stars in the Large Magellanic Cloud using the OGLE survey; and more
recently in the Kepler binary catalogue 3 paper (Kirk et al. 2014, in prep.), an extensive catalogue
of binary stars that contains 154 heartbeat stars, all observed using the Kepler satellite. Fig. 1 shows
a selection of heartbeat stars from the Kepler sample. These heartbeat stars were identiﬁed through
a e-mail: kmhambleton@uclan.ac.uk
   
 
DOI: 10.1051/
C©Owned by the authors, published by EDP Sciences, 2015
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201epjconf
EPJ Web of Conferences ,
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Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510104007
Fig. 1. A selection of heartbeat stars from the Kepler sample. Depicted are the time series (left panel) and phase
folded data (right panel). The phase folded data clearly depict the pulsations that are integer multiples of the
orbital frequency: tidally induced pulsations.
a combined eﬀort from the Heartbeat Star Team, the Planet Hunters, the Eclipsing Binary Working
Group and other independent sources.
2 Tidally Induced Pulsations
Tidally induced pulsations are stellar oscillations that are driven by the tidal force of the companion
star. In a binary system with an eccentric orbit, when a stellar eigenfrequency is close to a multiple of
the orbital frequency, the star can act like a forced oscillator, which causes an increase in the oscillation
amplitude of the mode (relative to non-resonant modes). The signature of tidally excited modes is
thus an oscillation frequency at a precise integer multiple of the orbital frequency. Approximately
20% of our current Kepler sample of heartbeat stars demonstrate tidally induced pulsations above our
detection limit.
Tidally induced pulsations have long been theorised (4; 5; 6) as a mechanism for the circulari-
sation of binary star orbits and the spin up of stars. However, until KOI-54, their presence has only
been speculated (7). The unquestionable nature of the tidally induced pulsations in KOI-54 sparked
the interest of many theorists and consequently three publications (8; 9; 10) appeared discussing the
physical nature of tidally induced pulsations and the relevance of the 90th and 91st orbital harmonic
- the two prominent pulsation frequencies in KOI-54. Fuller & Lai (8) proposed that the two highest
amplitude tidally induced pulsations were excited through a mechanism called resonant locking (cf.
§2.1). Burkart et al. (9) disputed this on the grounds that the torque produced by the proposed modes
was not enough to provide resonant locks and that it is unlikely that two resonant locks would occur
simultaneously. Later, O’leary & Burkart (10) showed that the 90th and 91st harmonic were likely
l = 2,m = 0 modes, which theory at the time suggested could not be resonantly locked. Another
interesting observation by O’leary & Burkart (10) was that all of the pulsation modes of KOI-54 are
EPJ Web of Conferences
04007-p.2
either tidally excited pulsations or their combinations, which was later found to be the case for all the
gravity (g) modes in KIC 4544587 (11).
2.1 Resonant Locking
The theory of resonantly excited modes – eigenmodes in resonance with the orbit – was suggested by
Witte and Savonije (12; 13) and again more recently by Kumar, Ao and Quataert (14) long before the
discovery of heartbeat stars. Due to the expected transient nature of resonant modes, it was not antic-
ipated that they would be observed. However, KOI-54 and KIC 8164262 (cf. Sect. 4) both have high
amplitude modes that are not easily explained by the forcing of the eigenfrequencies alone. Resonance
locking has been proposed as a mechanism that can “lock” a stellar eigenfrequency and the orbit in
resonance, thus extending the lifetime of the resonance and making observations of tidal resonance
possible. While the resonant locking of KOI-54 is currently under dispute, it has not been completely
ruled out. Moreover, KIC 8164262 has only a single high amplitude mode that is an l = 2,m = 2 mode,
which makes a stronger case for resonant locking.
The proposed mechanism of resonant locking is the following: as two stars in an eccentric conﬁgu-
ration orbit each other, the stellar orbit evolves through the transfer of energy and angular momentum,
causing the orbit and thus orbital period to get smaller and the stars spin faster. In parallel, the increase
in rotational velocity of the stars causes the stellar eigenfrequencies to change. Resonance locking
predicts that, when in resonance, these two eﬀects happen on an equal time scale such that the stellar
eigenfrequencies are locked to the changing orbital period. Thus, rather than passing through reso-
nance the tidally induced pulsations are locked in resonance with the orbit, enabling the observation
of resonantly excited modes.
3 Modelling Heartbeat Stars
As the parameter space of binary stars is highly irregular with many degeneracies and correlations,
we chose to combine emcee, an aﬃne invariant version of Markov chain Monte Carlo methods (mcmc)
(15) with phoebe, the binary modelling software package, which now has python scripting capabilities.
When modelling heartbeat stars we also ﬁt the tidally induced pulsations using sine waves by ﬁxing
the frequencies to a multiples of the orbital frequency and ﬁtting the amplitudes and phases.
To reduce the number of parameters in our models, at each iteration we calculate: the phase of the
periastron variation, the passband luminosity and the spin to orbital rotation frequency. To enhance
our models we also calculate the critical potentials at the Lagrangian points L1 and L2. Subsequently,
if there is no evidence of mass transfer, we use this as a constraint for our models and do not allow
the potential value to become smaller than the potential at the Lagrangian point L1. Alternatively, if
there is evidence of mass transfer (or for contact systems), we do not allow the stellar potentials to
become smaller than L2 as this creates a non-physical scenario where the model star has a dimple in
the side pointing away from the companion. The common geometry of heartbeat stars also make them
ideal candidates for Doppler boosting. Consequently we adjust the model ﬂux to account for Doppler
boosting using Eqn. 2 in Bloemen et al. (16), extended to account for boosting in both objects.
4 KIC8164262
KIC 8164262 is a highly eccentric (e ≈ 0.9), 13th magnitude heartbeat star in a ∼90 d orbit with
a single high amplitude (∼900 ppm) tidally induced pulsation that oscillates precisely 229 times per
orbit (cf. Fig.2). The primary component of KIC 8164262 is a late A/early F star with an M type
companion. This object was selected for detailed study as the prominent high amplitude mode was
suggestive of resonant locking. KIC 8164262 presents a plethora of tidally induced g modes ranging
from 120 to 320 cycles per orbit (∼1–4 d−1). However, the largest amplitude mode has an amplitude
twenty times greater than all other modes (900 ppm compared to the second highest at 45 ppm). We
04007-p.3
The Space Photometry Revolution 
0.998
0.999
1.000
1.001
1.002
F
lu
x
-0.001
0.000
0.001
-0.02 -0.01 0.00 0.01 0.02
Phase
Fig. 2. Upper panel: A phased light curve (black points) of KIC 8164262, a heartbeat star with a single high
amplitude pulsation. The model is overlayed in red and is comprised of the binary features and highest amplitude
pulsation. The periastron variation, centred on zero, has a similar amplitude to the highest amplitude pulsation.
Lower panel: the residuals of the binary model ﬁt to the phased data (black points). Only a fraction of the 90 d
orbit is shown for clarity.
used theoretical models of a star with equal mass (M1 = 1.9M), radius (R1 = 2.5R) and temperature
(Te f f ,1 = 7000K) to predict the expected combinations of frequency and amplitudes for resonantly
locked modes. These predictions are in good agreement with the frequency and amplitude of the 229th
harmonic.
References
1. W.F. Welsh, J.A. Orosz, C. Aerts, T.M. Brown, E. Brugamyer, W.D. Cochran, R.L. Gilliland, J.A.
Guzik, D.W. Kurtz, D.W. Latham et al., ApJS197, 4 (2011), 1102.1730
2. S.E. Thompson, M. Everett, F. Mullally, T. Barclay, S.B. Howell, M. Still, J. Rowe, J.L. Chris-
tiansen, D.W. Kurtz, K. Hambleton et al., ApJ753, 86 (2012), 1203.6115
3. C.P. Nicholls, P.R. Wood, MNRAS421, 2616 (2012), 1201.1043
4. J.P. Zahn, A&A41, 329 (1975)
5. P. Goldreich, P.D. Nicholson, ApJ342, 1079 (1989)
6. M.G. Witte, G.J. Savonije, A&A386, 222 (2002)
7. C. Maceroni, J. Montalba´n, E. Michel, P. Harmanec, A. Prsa, M. Briquet, E. Niemczura, T. Morel,
D. Ladjal, M. Auvergne et al., A&A508, 1375 (2009), 0910.3513
8. J. Fuller, D. Lai, MNRAS420, 3126 (2012), 1107.4594
9. J. Burkart, E. Quataert, P. Arras, N.N. Weinberg, MNRAS421, 983 (2012), 1108.3822
10. R.M. O’Leary, J. Burkart, MNRAS440, 3036 (2014), 1308.0016
11. K.M. Hambleton, D.W. Kurtz, A. Prsˇa, J.A. Guzik, K. Pavlovski, S. Bloemen, J. Southworth,
K. Conroy, S.P. Littlefair, J. Fuller, MNRAS434, 925 (2013), 1306.1819
12. M.G. Witte, G.J. Savonije, A&A350, 129 (1999), astro-ph/9909073
13. M.G. Witte, G.J. Savonije, A&A366, 840 (2001)
14. P. Kumar, C.O. Ao, E.J. Quataert, ApJ449, 294 (1995), arXiv:astro-ph/9503053
15. D. Foreman-Mackey, D.W. Hogg, D. Lang, J. Goodman, PASP125, 306 (2013), 1202.3665
16. S. Bloemen, T.R. Marsh, R.H. Østensen, S. Charpinet, G. Fontaine, P. Degroote, U. Heber, S.D.
Kawaler, C. Aerts, E.M. Green et al., MNRAS410, 1787 (2011), 1010.2747
EPJ Web of Conferences
04007-p.4


With the advent of high precision photometry from satellites such as Kepler and CoRoT, a whole new layer of interesting and astounding astronomical objects has been revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccentric ellipsoidal variables that undergo strong tidal interactions when the stars are almost in contact at the time of closest approach. These interactions deform of the stars and cause a notable light curve variation in the form of a tidal pulse. A subset of these objects (~20%) show prominent tidally induced pulsations: pulsations forced by the binary orbit. We now have a fully functional code that models binary star features (using PHOEB

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Heartbeat stars and the ringing of tidal pulsations

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